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CN111240202A - Online identification method for electro-hydraulic servo system of aero-engine - Google Patents

Online identification method for electro-hydraulic servo system of aero-engine Download PDF

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CN111240202A
CN111240202A CN202010050859.9A CN202010050859A CN111240202A CN 111240202 A CN111240202 A CN 111240202A CN 202010050859 A CN202010050859 A CN 202010050859A CN 111240202 A CN111240202 A CN 111240202A
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刘金鑫
杨亮东
宋志平
耿佳
陈雪峰
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Xian Jiaotong University
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Abstract

The invention discloses an online identification method for an electro-hydraulic servo system of an aircraft engine, which comprises the following steps: sensor measuring electrohydraulic servo system input x [ n ]]And an output d [ n ]]Estimating electrohydraulic servo system input x [ n ]]And an output d [ n ]]Based on the mean square value, estimating a filter compensation factor g [ n ] by an exponential smoothing method]Using IIR filter as the model of on-line identification, the system output is
Figure DDA0002369827810000011
According to the filter compensation factor g [ n ]]Computing the compensated output d' n of the system]=d[n]/g[n]And compensating the error e' [ n ]]=d′[n]‑y[n]Vector of parameters
Figure DDA0002369827810000012
Performing parameter adaptive update wn+1=wn+2μ·e′[n]·[βnαn]TAfter the parameter updating is finished, the actual output of the filter after being compensated is y' [ n ]]=g[n]y[n]The compensated filter parameters are
Figure DDA0002369827810000013

Description

Online identification method for electro-hydraulic servo system of aero-engine
Technical Field
The invention belongs to the technical field of control of aero-engines, and particularly relates to an online identification method for an electro-hydraulic servo system of an aero-engine.
Background
In an aircraft engine control system, an electro-hydraulic servo system is an important component and is responsible for fuel supply, guide vane angle control and nozzle area control of the aircraft engine. The precise control of the electro-hydraulic servo system is an important prerequisite for the safe operation of the aircraft engine. The accurate model is the basis for guaranteeing the control effect of the electro-hydraulic servo system, and in the running process of the aeroengine, the transmission characteristic of the electro-hydraulic servo system is time-varying due to variable working conditions of the engine. Generally, a transfer function of an electro-hydraulic servo system is identified through a real-time filter, and the electro-hydraulic servo system is a typical amplification system, so that the magnitude difference between input current and output displacement of the electro-hydraulic servo system is large, and the magnitude difference between input data for identification is too large in the system identification process, so that the convergence of adaptive parameters is not facilitated. In order to solve this problem, input and output data need to be calibrated to determine respective magnitudes, and data normalization is performed in advance. However, the method cannot be carried out on line, so that a novel online system identification method which can solve the problem of magnitude inconsistency between system input data and does not need data calibration is needed, the convergence speed and the identification precision of an online filter are further improved, and a more accurate and reliable model basis is provided for the control of an electro-hydraulic servo system of an aeroengine.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
In order to solve the problems that the traditional system identification method is poor in convergence under the condition that the modeling data magnitude is inconsistent and avoid the complex process of off-line data calibration, the invention provides an aeroengine electro-hydraulic servo system identification on-line method without data calibration. On the basis of the traditional online system identification method, a self-adaptive compensation factor is added, the compensation factor carries out self-adaptive adjustment through the input and output data of a real-time estimation system, and the compensation factor is utilized to carry out online correction on the modeling data for system identification, so that the magnitude of the modeling data is consistent, namely the modeling data is regularized, and the convergence speed and the identification precision of the online identification algorithm of the system are finally improved. And a more accurate and reliable model foundation is provided for an electro-hydraulic servo system of the aero-engine.
The invention aims to realize the purpose through the following technical scheme, and the online identification method of the electro-hydraulic servo system of the aero-engine comprises the following steps:
in the first step, the sensor measures the input x n and output d n of the electrohydraulic servo system,
in the second step, the electrohydraulic servo system input x [ n ] is estimated]And an output d [ n ]]Mean square value of
Figure BDA0002369827790000021
Figure BDA0002369827790000022
Wherein N iswIn order to estimate the length of the window,
in the third step, based on the mean square value, a filter compensation factor g [ n ] is estimated by an exponential smoothing method],
Figure BDA0002369827790000023
Where λ is the smoothing factor, eps is a positive number to prevent zero division,
in the fourth step, an IIR filter is used as an online identification model, the system output is,
Figure BDA0002369827790000031
wherein, x [ n ]]Being the filter input, y [ n ]]Is the filter output, naIs an output order of nbTo input the order, aiAnd bjFor the parameters of the adaptation of the filter,
in a fifth step, a compensation output d ' n ═ d [ n ]/g [ n ] and a compensation error e ' n ═ d ' n ═ y [ n ] of the system are calculated based on the filter compensation factor g [ n ],
in the sixth step, a vector is set
Figure BDA0002369827790000036
And
Figure BDA0002369827790000032
wherein each element is iteratively updated according to the following formula,
Figure BDA0002369827790000033
in the seventh step, a parameter vector is set
Figure BDA0002369827790000034
Performing parameter adaptive update wn+1=wn+2μ·e'[n]·[βnαn]TWhere μ is the learning step size,
in the eighth step, after the parameter updating is completed, the actual output of the filter after compensation is y' [ n ]]=g[n]y[n]The compensated filter parameters are
Figure BDA0002369827790000035
Wherein bj=g[n]·bj
In the method, the identified electro-hydraulic servo system is described by a third-order model, and the transfer function of the discrete form is shown as the following formula:
Figure BDA0002369827790000041
wherein the sampling time is 1 ms.
In the method, in the second step, the window length N is estimatedwIs 50.
In the method, wherein, in the third step, the smoothing factor λ is 0.999 and the eps is 1 × 10-8
In the method, in the fourth step, the order n is inputbAnd output order naAre all 3.
In the method, in the seventh step, the learning step size μ is 0.005.
In the method, a modeling signal x [ n ] is a zero-mean Gaussian white noise sequence of unit variance.
Compared with the prior art, the invention has the following advantages:
the online identification method of the aero-engine electro-hydraulic servo system based on the adaptive compensation factor can ensure that the system identification parameters can be converged quickly and stably without a data calibration process under the condition that the magnitude difference of system input and output data is large, and has higher convergence speed and higher identification precision compared with the traditional system identification method.
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Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a structural diagram of an online identification method of an aero-engine electro-hydraulic servo system without data calibration according to the invention;
FIG. 2 is a comparison graph of error curves of an online identification process according to an embodiment of the present invention;
FIG. 3 is a comparison chart of online parameter identification results according to an embodiment of the present invention.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 3. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, the online identification method of the electro-hydraulic servo system of the aero-engine comprises the following steps:
in a first step S1, a sensor measures an electro-hydraulic servo system input x [ n ] and output d [ n ],
in a second step S2, electrohydraulic servo system inputs x [ n ] are estimated]And an output d [ n ]]Mean square value of
Figure BDA0002369827790000061
Figure BDA0002369827790000062
Wherein N iswIn order to estimate the length of the window,
in a third step S3, a filter compensation factor g [ n ] is estimated based on the mean square value by means of exponential smoothing],
Figure BDA0002369827790000063
Where λ is the smoothing factor, eps is a positive number to prevent zero division,
in a fourth step S4, using the IIR filter as a model for online identification, the system output is,
Figure BDA0002369827790000071
wherein, x [ n ]]Being the filter input, y [ n ]]Is the filter output, naIs an output order of nbTo input order, αiAnd bjFor the parameters of the adaptation of the filter,
in a fifth step S5, a compensation output d ' [ n ] ═ d [ n ]/g [ n ] and a compensation error e ' [ n ] ═ d ' [ n ] -y [ n ] of the system are calculated based on the filter compensation factor g [ n ],
in a sixth step S6, a vector is set
Figure BDA0002369827790000072
And
Figure BDA0002369827790000073
wherein each element is iteratively updated according to
Figure BDA0002369827790000074
In the seventh step S7, a parameter vector is set
Figure BDA0002369827790000075
Performing parameter adaptive update wn+1=wn+2μ·e′[n]·[βnαn]TWhere μ is the learning step size,
in the eighth step S8, after the parameter update is completed, the filter is compensatedIs the actual output of y' [ n ]]=g[n]y[n]The compensated filter parameters are
Figure BDA0002369827790000076
Wherein bj=g[n]·bj
The invention adopts a self-adaptive compensation factor based on the real-time estimation of input and output data to regularize the data used for system modeling, thereby improving the convergence speed and the identification precision of the system online identification algorithm.
In a preferred embodiment of the method, the identified electro-hydraulic servo system is described by a third-order model, and the discrete transfer function is shown as follows:
Figure BDA0002369827790000081
wherein the sampling time is 1 ms. Supplementary unspecified alphabetical meanings
In a preferred embodiment of the method, in a second step S2, the window length N is estimatedwIs 50.
In a preferred embodiment of the method, in a third step S3, the smoothing factor λ is 0.999 and the eps is 1 × 10-8
In a preferred embodiment of the method, in the fourth step S4, the order n is inputbAnd output order naAre all 3.
In a preferred embodiment of the method, in the seventh step S7, the learning step size μ is 0.005.
In a preferred embodiment of the method, the modeling signal x [ n ] is a zero-mean white gaussian noise sequence of unit variance.
For further understanding of the present invention, in one embodiment, as shown in fig. 1, the online identification method of the present invention includes the following steps:
s1, using the sensor to measure the system input x [ n ] and output d [ n ].
S2, estimating the mean square value of the system input data and the system output data
Figure BDA0002369827790000091
Figure BDA0002369827790000092
Wherein N iswTo estimate the window length.
S3, estimating filter compensation factor g [ n ] by exponential smoothing method according to the mean square value of the input and output data of the system, the concrete process is as follows
Figure BDA0002369827790000093
Where λ is the smoothing factor and eps is a small positive number to prevent zero division.
S4, using IIR filter as the model of system identification, the system output can be expressed as
Figure BDA0002369827790000094
Wherein, x [ n ]]For filter input data, y [ n ]]For the filter output data, naIs an output order of nbTo input the order, aiAnd bjThe parameters are adapted for the filter.
S5, calculating a compensation output d ' n ═ d [ n ]/g [ n ] and a compensation error e ' n ═ d ' n ═ y [ n ] of the system according to the filter compensation factor g [ n ].
S6, defining vector
Figure BDA0002369827790000095
And
Figure BDA0002369827790000096
wherein each element is iteratively updated according to
Figure BDA0002369827790000101
S7, defining parameter vector
Figure BDA0002369827790000102
Performing parameter adaptive update wn+1=wn+2μ·e'[n]·[βnαn]TWhere μ is the learning step size.
S8, after the parameter updating is finished, the actual output of the filter after being compensated is y' [ n ]]=g[n]y[n]The compensated filter parameters are
Figure BDA0002369827790000103
Wherein bj=g[n]·bj
In one embodiment, the identified aero-engine electro-hydraulic servo system is described by a third order model whose discrete form transfer function is shown as:
Figure BDA0002369827790000104
wherein the sampling time is 1 ms. The modeling signal x n is a zero mean white Gaussian noise sequence of unit variance.
In this embodiment, in a first step S1, the system input x [ n ] and output d [ n ] are measured with sensors.
In this embodiment, in a second step S2, the mean square value of the system input data and output data is estimated
Figure BDA0002369827790000105
Figure BDA0002369827790000111
Wherein the window length Nw=50。
In this embodiment, in the third step S3, the filter compensation factor g [ n ] is estimated by exponential smoothing according to the mean square value of the system input/output data, as shown below
Figure BDA0002369827790000112
Wherein λ is 0.999, eps is 1 × 10-8
In this embodiment, in the fourth step S4, using the IIR filter as a model for system identification, the input and output orders are na=nbThe input-output delay is 1 unit, and the system output can be expressed as 3
Figure BDA0002369827790000113
In this embodiment, in a fifth step S5, a compensation output d ' [ n ] = d [ n ]/g [ n ] and a compensation error e ' [ n ] ═ d ' [ n ] -y [ n ] of the system are calculated based on the filter compensation factor g [ n ].
In this embodiment, in the sixth step S6, a vector is specified
Figure BDA0002369827790000114
And
Figure BDA0002369827790000115
wherein each element is iteratively updated according to
Figure BDA0002369827790000121
In this embodiment, in the seventh step S7, a parameter vector is specified
Figure BDA0002369827790000122
Performing parameter adaptive update wn+1=wn+2μ·e′[n]·[βnαn]TWherein the learning step size μ is 0.005.
In this embodiment, in the eighth step S8, after the parameter update is completed, the actual output of the filter after compensation is y' [ n ]]=g[n]y[n]The compensated filter parameters are
Figure BDA0002369827790000123
Wherein bj=g[n]·bj
FIG. 2 is a graph comparing error curves of an online identification process according to an embodiment of the present invention. All the results are obtained through 100 Monte Carlo simulations, and compared with the traditional identification method, the online system identification method based on the adaptive compensation factors has higher convergence speed and higher identification precision.
FIG. 3 is a comparison chart of online parameter identification results according to an embodiment of the present invention. It can be seen that the traditional identification method is difficult to identify accurate system parameters; the online identification method based on the adaptive compensation factor can accurately identify the system parameters.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (7)

1. An online identification method for an electro-hydraulic servo system of an aircraft engine comprises the following steps:
in a first step (S1), a sensor measures an input x [ n ] at time n and an output d [ n ] at time n of an electro-hydraulic servo system,
in a second step (S2), an electrohydraulic servo system input x [ n ] is estimated]And an output d [ n ]]Mean square value of
Figure FDA0002369827780000011
Figure FDA0002369827780000012
Wherein, X [ n ]]Representing the mean square value of the input at time n, Dn]Representing the mean square of the output at time N, NwIn order to estimate the length of the window,
in a third step (S3), a filter compensation factor g [ n ] is estimated by exponential smoothing based on the mean square value],
Figure FDA0002369827780000013
Where λ is the smoothing factor, eps is a positive number to prevent zero division,
in the fourth step (S4), using the IIR filter as a model for online identification, the system output is,
Figure FDA0002369827780000014
wherein, x [ n ]]Being the filter input, y [ n ]]Is the filter output, naIs an output order of nbTo input the order, aiAnd bjFor the adaptive parameters of the filter, i is 1 to naJ is any integer from 0 to nb-any integer between 1 and-1,
in a fifth step (S5), a compensation output d ' [ n ] ═ d [ n ]/g [ n ] and a compensation error e ' [ n ] ═ d ' n ] -y [ n ] of the system are calculated based on the filter compensation factor g [ n ],
in the sixth step (S6), a vector is set
Figure FDA0002369827780000021
And
Figure FDA0002369827780000022
t in the superscript denotes the matrix transpose and n in the subscript denotes the time instant, wherein each element in the vector is iteratively updated according to the following formula,
Figure FDA0002369827780000023
wherein k is 1 to naI is 1 to naJ is any integer from 0 to nb-any integer between 1, αi[n]Representation vector αnβj[n]Representation vector βnα th element of (1)i[n-k]Representation vector αn-kβj[n-k]Representation vector βn-kThe (c) th element of (a),
in the seventh step (S7), a parameter vector is set
Figure FDA0002369827780000024
Performing parameter adaptive update wn+1=wn+2μ·e′[n]·[βnαn]TWhere μ is the learning step size, the subscript n denotes the time,
in the eighth step (S8), after the parameter update is completed, the actual output of the filter after compensation is y' [ n ]]=g[n]y[n]The compensated filter parameters are
Figure FDA0002369827780000025
Wherein bj=g[n]·bj,g[n]For the filter compensation factor, aiAnd bjIs the original parameter vector wnI is 1 to naJ is any integer from 0 to nb-1 or higher.
2. The method of claim 1, wherein the identified electro-hydraulic servo system is described by a third order model, the discrete form of which is the transfer function H (z)-1) As shown in the following formula:
Figure FDA0002369827780000031
of these, preferred is z-1,z-2,z-3Both represent delay operators in the transfer function with a sampling time of 1 ms.
3. The method according to claim 1, wherein in the second step (S2), the window length N is estimatedwIs 50.
4. The method according to claim 1, wherein, in the third step (S3), the smoothing factor λ is 0.999 and the eps is 1 x 10-8
5. The method as claimed in claim 1, wherein, in the fourth step (S4), the order n is inputaAnd output order nbAre all 3.
6. The method according to claim 1, wherein in the seventh step (S7), the learning step size μ is 0.005.
7. The method of claim 1, wherein the modeled signal x [ n ] is a zero-mean white gaussian noise sequence of unit variance.
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